Seminar (post-master course):
Relativity, and the Global
Systems (Galileo and GPS)
Tarantola (web page, e-mail) & Bartolomé Coll (web page, e-mail)
with the contribution of José-Maria
- Click here to download the
program of the seminar.
- Please click here to see
the list of students.
- Some texts of possible interest are posted here.
- Introduction to Tensor Calculus
introduction to Special Relativity (slides).
- The first two lessons (text).
- Third lesson Introduction to
Differential Geometry (text)
- An excellent small text on Differential
Geometry, written by our
dear friend André Heslot (1954-2000): Géométrie
- Flash introduction to Gravimetry
- Relativistic Corrections in the
GPS System (slides).
- Introduction to General
Relativity I (slides).
- Introduction to General
Relativity II (Schwarzscild, Kerr, UAI coordinates) (slides).
- UAI Resolution on Reference
Frames (English) (French).
- Coordinate Systems in (General)
- Emission Coordinates as
Positioning Systems (slides).
- Flash introduction to Inverse
Note that Tarantola's book on Inverse
Problems is available for free download (tarantola.cc).
- Formulation of the
Relativistic Positioning and Gravimetry Problem (slides)
While today's presentations of
gravimetry still use a Newtonian
veiwpoint of the space-time, the gravity field is, and only is, the
space-time metric. Gravimetry is gravitation, and gravitation theory is
the science of the geometry of space-time. In this course, we shall
examine the conceptual foundations of relativistic gravimetry. Which
kind of (relativistic) coordinates are accessible to experiment? Which
kind of measurements may bring information on the space-time metric?
The development of the theory has strong implications for the Global
Navigation Satellite Systems (Galileo or the GPS): while these systems
are today operated as if the space-time was Newtonian, using relativity
just as a set of "corrections", one may imagine an entirely, fully
relativistic, way of operation. Such a system would constitute the
ultimate gravimeter. The emphasis of the course will be in the theory,
not in the applications.
Requirements for the
part may have a very variable length, to adapt to the median background
of the students, but some familiarity with special relativity and
tensor calculus will be of great help. This will essentially be a
theoretical seminar. Although we shall have a very precise application
in mind (the GNSS and gravimetry) the theory to be developed shall not
have an immediate use: present day practices are quite far from being
based in good theory. We do think that, some day, the GNSS systems and
the gravimetric satellites will be operated in this way, but it may
take a long time before the proposed ideas come into normal use.
Only theoretically minded
students should attend the course. If
you don't like theory or you don't like mathematics, please don't try
to attend this seminar.